The PX70 motorcycle was a motorcycle type dating back to the 22nd century. One of these bikes was stored aboard the USS Franklin at the time of its crash landing on Altamid.
George Kirk, a 23rd century Starfleet officer, owned a PX70 prior to his death. His widow, Winona, told her son James that George would drive it with her seated behind him, which would drive her nuts.
In 2263, while stranded on Altamid, Jim Kirk noticed a PX70 in the Franklin's mess hall. He rode the motorcycle as a distraction while his officers rescued the former crew of the USS Enterprise from Krall's camp. To increase the confusion, several holographic replicas of himself and the vehicle were created, all headed in different directions. (Star Trek Beyond)
At least two PX70 motorcycles were used in the production of Star Trek Beyond, painted green and featuring Military Assault Command Operations/USS Franklin insignias signifying their official use by the MACO organization. [1]
In the special features for Beyond, it is stated that the PX70 manufacturer is named Hilts, after Steve McQueen's character in The Great Escape.
The real life motorcycle type used in the film was a BamX BX-70.